The routine reduces the target of M by elementary moves (see elementary) involving just d+1 variables. The outcome is probabalistic, but if the routine fails, it gives an error message.
i1 : kk=ZZ/32003 o1 = kk o1 : QuotientRing |
i2 : S=kk[a..e] o2 = S o2 : PolynomialRing |
i3 : i=ideal(a^2,b^3,c^4, d^5) 2 3 4 5 o3 = ideal (a , b , c , d ) o3 : Ideal of S |
i4 : F=res i 1 4 6 4 1 o4 = S <-- S <-- S <-- S <-- S <-- 0 0 1 2 3 4 5 o4 : ChainComplex |
i5 : f=F.dd_3 o5 = {5} | c4 d5 0 0 | {6} | -b3 0 d5 0 | {7} | a2 0 0 d5 | {7} | 0 -b3 -c4 0 | {8} | 0 a2 0 -c4 | {9} | 0 0 a2 b3 | 6 4 o5 : Matrix S <--- S |
i6 : EG = evansGriffith(f,2) -- notice that we have a matrix with one less row, as described in elementary, and the target module rank is one less. o6 = {5} | c4 d5 0 {6} | -b3 0 d5 {7} | 0 -b3 -6088a4+8155a3b-3172a2b2-3567a3c-7154a2bc-5884a2c2-c4 {7} | a2 0 1016a4+7359a3b-9571a2b2+1439a3c+3564a2bc+3266a2c2 {8} | 0 a2 2183a3-7220a2b-14451a2c ------------------------------------------------------------------------ 0 | 0 | -6088a2b3+8155ab4-3172b5-3567ab3c-7154b4c-5884b3c2 | 1016a2b3+7359ab4-9571b5+1439ab3c+3564b4c+3266b3c2+d5 | 2183ab3-7220b4-14451b3c-c4 | 5 4 o6 : Matrix S <--- S |
i7 : isSyzygy(coker EG,2) o7 = true |